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Set of unordered triples from a vertex set
the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have
Two-graph
Procedures for constructing new graphs in graph theory
of graph theory, graph operations are operations which produce new graphs from initial ones. They include both unary (one input) and binary (two input)
Graph_operations
Operation that combines two graphs
In graph theory, the join operation is a graph operation that combines two graphs by connecting every vertex of one graph to every vertex of the other
Join_(graph_theory)
Concept in graph theory
In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0
Strongly_regular_graph
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Cubic graph with 10 vertices and 15 edges
bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the
Petersen_graph
Binary operation combining the vertex and edge sets of two graphs
In graph theory, a branch of mathematics, the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph. It is
Disjoint_union_of_graphs
Topics referred to by the same term
A two-dimensional graph may refer to The graph of a function of one variable A planar graph A diagram in a plane This disambiguation page lists mathematics
Two-dimensional_graph
1950 novel
The Two Graphs is a 1950 detective novel by John Rhode, the pen name of the British writer Cecil Street. It is the fiftieth in his long-running series
The_Two_Graphs
Methodic assignment of colors to elements of a graph
certain constraints, such as that no two adjacent elements have the same color. Graph coloring is a special case of graph labeling. In its simplest form, it
Graph_coloring
Bijection between the vertex set of two graphs
In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f : V ( G ) → V ( H ) {\displaystyle f\colon V(G)\to
Graph_isomorphism
Graph divided into two independent sets
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets
Bipartite_graph
Graph of chess rook moves
In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's
Rook's_graph
Graph with nodes connected in a closed chain
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if
Cycle_graph
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
Graph of king moves on a chessboard
In graph theory, a king's graph is a graph that represents all legal moves of the king chess piece on a chessboard where each vertex represents a square
King's_graph
Concept in quantum computing
computing, a graph state is a special type of multi-qubit state that can be represented by a graph. Each qubit is represented by a vertex of the graph, and there
Graph_state
Non-crossing graph with vertices on outer face
face of the drawing. Outerplanar graphs may be characterized (analogously to Wagner's theorem for planar graphs) by the two forbidden minors K4 and K2,3,
Outerplanar_graph
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
Adjacent subset of an undirected graph
In graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are
Clique_(graph_theory)
Heuristic test for graph isomorphism
In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. It is
Weisfeiler Leman graph isomorphism test
Weisfeiler_Leman_graph_isomorphism_test
Database using graph structures for queries
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key
Graph_database
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
In graph theory, a circulant graph is an undirected graph acted on by a cyclic group of symmetries which takes any vertex to any other vertex. It is sometimes
Circulant_graph
Graph representing edges of another graph
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges
Line_graph
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
Vertices connected in pairs by edges
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some
Graph_(discrete_mathematics)
Gluing graphs at complete subgraphs
In graph theory, a branch of mathematics, a clique sum (or clique-sum) is a way of combining two graphs by gluing them together at a clique, analogous
Clique-sum
Graph with oriented edges
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed
Directed_graph
Graph defined from a mathematical group
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract
Cayley_graph
One of two different regular graphs with 16 vertices
field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with
Clebsch_graph
Operation in graph theory
In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and
Cartesian_product_of_graphs
Directed graph representing dependencies
mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other
Dependency_graph
On coloring the edges of graphs
degree Δ of the graph. At least Δ colors are always necessary, so the undirected graphs may be partitioned into two classes: "class one" graphs for which Δ
Vizing's_theorem
Graph of triangles with a shared vertex
the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and
Friendship_graph
Property of graphs that depends only on abstract structure
In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations
Graph_property
On existence of a strongly regular graph
exists an undirected graph with 99 vertices, in which each two adjacent vertices have exactly one common neighbor, and in which each two non-adjacent vertices
Conway's_99-graph_problem
Geometric graph with unit edge lengths
particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever
Unit_distance_graph
Length of shortest path between two nodes of a graph
mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting
Distance_(graph_theory)
Trail in a graph that visits each edge once
graph has an Euler cycle if and only if every vertex has an even number of incident edges. The term Eulerian graph has two common meanings in graph theory
Eulerian_path
Linear algebra aspects of graph theory
associated to the graph, such as the Colin de Verdière number. Two graphs are called cospectral or isospectral if the adjacency matrices of the graphs are isospectral
Spectral_graph_theory
Cycle graph plus universal vertex
In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can
Wheel_graph
Graphs that differ only by edge subdivision
In graph theory, two graphs G {\displaystyle G} and G ′ {\displaystyle G'} are homeomorphic if there is a graph isomorphism from some subdivision of G
Homeomorphism_(graph_theory)
Graphs formed by a hypercube's edges and vertices
In graph theory, the hypercube graph Q n {\displaystyle Q_{n}} is the edge graph of the n {\displaystyle n} -dimensional hypercube, that is, it is the
Hypercube_graph
Graph with sign-labeled edges
In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if
Signed_graph
Binary operation in graph theory
In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they
Strong_product_of_graphs
In polytope theory, the edge graph (also known as vertex-edge graph or just graph) of a polytope is a combinatorial graph whose vertices and edges correspond
Graph_of_a_polytope
Graph that can be embedded in the plane
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect
Planar_graph
Regular graph with girth more than twice its diameter
Does a Moore graph with girth 5 and degree 57 exist? More unsolved problems in mathematics In graph theory, a Moore graph is a regular graph whose girth
Moore_graph
Structure-preserving correspondence between node-link graphs
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a
Graph_homomorphism
3-regular graph with no 3-edge-coloring
In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three
Snark_(graph_theory)
Graph made from vertices and edges of a convex polyhedron
In geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron
Polyhedral_graph
Subdivision of vertices into disjoint sets
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges
Graph_partition
Graph whose vertices correspond to combinations of a set of n elements
In graph theory, the Kneser graph K(n, k) (alternatively KGn,k) is the graph whose vertices correspond to the k-element subsets of a set of n elements
Kneser_graph
Graph related to another graph by a covering map
In the mathematical discipline of graph theory, a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to
Covering_graph
Query language for property graphs
GQL (Graph Query Language) is a standardized query language for property graphs first described in ISO/IEC 39075, released in April 2024 by ISO/IEC. The
Graph_Query_Language
Mathematical game played on a graph
pebbling moves. A pebbling move on a graph consists of choosing a vertex with at least two pebbles, removing two pebbles from it, and adding one to an
Graph_pebbling
Visualization of node-link graphs
and information visualization to derive two-dimensional (or, sometimes, three-dimensional) depictions of graphs arising from applications such as social
Graph_drawing
Square matrix used to represent a graph or network
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether
Adjacency_matrix
Cubic graph with 28 vertices and 42 edges
field of graph theory, the Coxeter graph is a 3-regular graph with 28 vertices and 42 edges. It is one of the 13 known cubic distance-regular graphs. It is
Coxeter_graph
Fundamental unit of which graphs are formed
specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set
Vertex_(graph_theory)
Graph where all long cycles have a chord
but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices. The chordal graphs may also be
Chordal_graph
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
Planar graph with 5 nodes and 6 edges
mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices
Butterfly_graph
Graph with tight clique-coloring relation
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every
Perfect_graph
mathematical field of graph theory, the Ellingham–Horton graphs are two 3-regular graphs on 54 and 78 vertices: the Ellingham–Horton 54-graph and the Ellingham–Horton
Ellingham–Horton_graph
Measure of similarity between two graphs
computer science, graph edit distance (GED) is a measure of similarity (or dissimilarity) between two graphs. The concept of graph edit distance was first
Graph_edit_distance
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
the diagonal. This is the Seidel adjacency matrix of a two-graph. Conversely, every two-graph can be represented as a set of equiangular lines. The problem
Equiangular_lines
Mapping a graph onto itself without changing edge-vertex connectivity
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving
Graph_automorphism
Representation of a mathematical function
In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where f ( x ) = y . {\displaystyle
Graph_of_a_function
In structure mining, a graph kernel is a kernel function that computes an inner product on graphs. Graph kernels can be intuitively understood as functions
Graph_kernel
Subgraph with contracted edges
In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting
Graph_minor
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Describing a family of graphs by excluding certain (sub)graphs
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to
Forbidden graph characterization
Forbidden_graph_characterization
Graph whose embedding in a Euclidean space forms a regular tiling
In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space R n {\displaystyle \mathbb {R}
Lattice_graph
Basic concept of graph theory
concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more
Connectivity_(graph_theory)
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first
Complete_bipartite_graph
Mathematical graph relating to chess
In graph theory, a knight's graph, or a knight's tour graph, is a graph that represents all legal moves of the knight chess piece on a chessboard. Each
Knight's_graph
Bipartite 4-regular graph with 20 nodes and 40 edges
mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking
Folkman_graph
Graph in graph theory
In graph theory, the lexicographic product or (graph) composition G ∙ H of graphs G and H is a graph such that the vertex set of G ∙ H is the cartesian
Lexicographic product of graphs
Lexicographic_product_of_graphs
Undirected graph with 14 vertices
mathematical field of graph theory, the Heawood graph is an undirected graph with 14 vertices and 21 edges, named after Percy John Heawood. The graph is cubic, and
Heawood_graph
Graph able to be partitioned into multiple independent sets
In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently
Multipartite_graph
Unsolved problem in computational complexity theory
isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. The problem is not known to be solvable in polynomial
Graph_isomorphism_problem
Binary operation on graphs
graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G1 and G2 and produces a graph H
Graph_product
In graph theory, the Berlekamp–Van Lint–Seidel graph is a locally linear strongly regular graph with parameters ( 243 , 22 , 1 , 2 ) {\displaystyle (243
Berlekamp–Van Lint–Seidel graph
Berlekamp–Van_Lint–Seidel_graph
Graph representing connectivity between cliques of another graph
simplex graph of a complete graph is a hypercube graph, and the simplex graph of a cycle graph of length four or more is a gear graph. The simplex graph of
Simplex_graph
Task in computational graph theory
In graph theory, a branch of mathematics, graph canonization is the problem of finding a canonical form of a given graph G. A canonical form is a labeled
Graph_canonization
Assignment of labels to elements of a graph
discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. Formally
Graph_labeling
Class of mathematical games
related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use
Graph_coloring_game
Longest distance between two vertices
In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of
Diameter_(graph_theory)
Graph in which every two vertices are adjacent
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique
Complete_graph
Intersection graph of trapezoids between parallel lines
In graph theory, trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. They are a class of co-comparability graphs that
Trapezoid_graph
testing whether two graphs are isomorphic. While it solves graph isomorphism on almost all graphs, there are graphs such as all regular graphs that cannot
Colour_refinement_algorithm
Planar, undirected graph with 2n vertices and 3n-2 edges
mathematical field of graph theory, the ladder graph Ln is a planar, undirected graph with 2n vertices and 3n − 2 edges. The ladder graph can be obtained as
Ladder_graph
Graph of numbers differing by a square
Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic
Paley_graph
Graph whose shortest paths are unique
In graph theory, a geodetic graph is an undirected graph such that there exists a unique (unweighted) shortest path between each two vertices. Geodetic
Geodetic_graph
Two special graphs in graph theory
In the mathematical field of graph theory, the Klein graphs are two different but related regular graphs, each with 84 edges. Each can be embedded in
Klein_graphs
Problem of finding similarity between graphs
Graph matching is the problem of finding a similarity between graphs. Graphs are commonly used to encode structural information in many fields, including
Graph_matching
Undirected, connected, and acyclic graph
undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or
Tree_(graph_theory)
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